Radiotherapy is commonly applied to treat cancerous tumors. During a radiotherapy session, a patient is subject to ionizing or non-ionizing radiation, which is designed to control or kill malignant cancerous cells. In addition to treating cancerous cells, however, radiotherapy may cause undesired side effects to the patient by damaging normal or healthy cells that are in proximity to the malignant cancerous cells in humans or animals. During radiotherapy, radioactive particles enter the patient's body and interact with the tissue and organs of the patient through radiation transport. Radiation transport refers to a process in which the radioactive particles transfer energy to the patient's body through the interaction with the tissue and organ, thereby subjecting the patient's body to radiation. Although mechanisms are employed to reduce radiation imparted to normal cells during radiotherapy, it is desired to simulate the radiation transport to estimate the amount of energy that the patient will receive before a treatment session, in order to facilitate treatment planning and management.
A Monte Carlo simulation is a commonly used method for simulating radiation transport in radiotherapy. According to the Monte Carlo simulation, the interactions between particles, such as photons or electrons, and patient's body are modeled as a stochastic process. The particle interactions are randomly sampled based on material properties of the tissues, in which the particles travel. These properties include, for example, mass stopping powers and mass scattering powers for charged particles, and mass attenuation coefficients for various types of discrete particle interaction.
In a conventional Monte Carlo simulation, the patient's body is modeled as a three-dimensional data set including a plurality of voxels. Each voxel may represent a value on a regular grid in three-dimensional space. Material information representing physical and material properties is defined for every voxel of the patient model. Based on the material information, the radiation transport may be determined by determining the distance traveled by a particular particle and the type of interaction between the particle and the voxels.
Two conventional approaches have been used to define the material information in a Monte Carlo simulation. One approach is the “no material” approach, where data representing physical properties is tabulated as a function of energy for water only. The data is then modified in each voxel on the basis of the mass density of the voxel with respect to the mass density of water. This approach, however, is typically very inflexible and does not allow the user to assign a specific medium to a particular voxel, in which the exact material composition is known. Furthermore, the “no material” approach may introduce significant systematic error in simulations, when metals or other high-atomic-number materials are present.
Another conventional approach is the “discrete material” approach, where every voxel is explicitly identified as containing a single defined material. A material may include a single element or several elements, whose proportions are specified either by mass for a mixture or by the number of atoms for a compound. However, a material medium is assigned to each patient voxel based solely on the information gathered during imaging.
As a result, the “discrete material” approach introduces discretization errors into the dose computation. For example, two voxels whose densities are respectively 1.100 g/cc and 1.102 g/cc are expected to have very similar material properties. However, the “discrete material” approach may characterize the former voxel to be soft tissue and the latter voxel to be bone. These two voxels include different materials with different mass densities and may interact differently with radioactive particles having the same energy.
In addition, the “discrete material” approach may cause discontinuous mappings between dose to medium (DTM) and dose to water (DTW). The choice between DTM and DTW affects which quantity is determined during the simulation, and thus, ultimately what is presented to the user. In the case of DTM, the actual deposited energy per unit mass received by the actual material is determined. In the case of DTW, the dose to a very small water volume embedded in the medium is determined. Conventional Monte Carlo algorithms may compute DTM, but historical dose algorithms frequently approximated tissue as water. The American Association of Physicists in Medicine has recommended that all radiotherapy planning systems report both DTM and DTW. Thus, a conversion between DTM and DTW is then often necessary. In the above example, the DTW/DTM ratio is about 1.01 for the purported “soft tissue” voxel and about 1.12 for the purported “bone” voxel. A difference of 11% in the DTM/DTW ratio may thus arise from a miniscule difference in mass density. To make the conversion between DTM and DTW smooth, new materials must be introduced that are gradated mixtures of soft tissue and bone. At least ten intermediate mixtures of soft tissue and bone must be defined in order to ensure that the discontinuity in the DTW/DTM ratio is never more than 1%.
As is evident from the foregoing, conventional techniques for simulating radiation transport for radiotherapy have several drawbacks. Accordingly, improvements in radiation transport for radiotherapy that overcome these drawbacks are needed.